In the geometric sequence with a first term of $6$ and a second term of $-6$, what is the $205^{th}$ term?
Answer: The common ratio of this sequence is $-1$.  The first few terms will be: $$6,-6,6,-6,...$$All even numbered terms have value $-6$, and all odd numbered terms have value $6$.  Since 205 is odd, its value will be $\boxed{6}$.